Getting Started with FEniCSx – Bibekananda Datta

What is `FEniCSx`

FEniCSx is an open source multi-platform computing environment to solve partial differential equations using finite element method. FEniCSx supports parallel computing with Python and C++ interface. FEniCSx is comprised of the libraries UFL, Basix, FFCx and DOLFINx which are the build blocks of it.

The project originally started in 2003 and was known as FEniCS. In 2020, the developers released a new version of the library which they renamed as FEniCSx. The latest stable version of legacy FEniCS was released on April 2019 and its barely updated. But many tutorials and legacy codes are perhaps written in legacy FEniCS. So you may want to install a version of it. We will demonstrate installing both versions on multiple different platforms here.

Both FEniCSx and FEniCS are available on Linux, macOS, and Windows. You can download and install it in different ways. Check out the options here for FEniCSx: https://github.com/FEniCS/dolfinx and here for legacy FEniCS: https://fenicsproject.org/download/archive/. For both versions, our preferred approach is to install them via Anaconda.

Installation on Windows

This step in only applicable if you are using Windows. You will have to set up Windows Subsystem for Linux (WSL) to use Anaconda based installation of FEniCSx and legacy FEniCS. WSL is a virtual Linux environment within Windows which allows you to use Linux command line tools and GUI applications. If you are on macOS or Linux, you can skip this step. If you are on Windows and already have installed WSL, it still might be interesting to download the recommended applications/ tools, such as VS Code.

Get your tools ready first

PowerShell 7

Microsoft Windows already comes with Windows PowerShell 5.1, but the modern edition of PowerShell 7 is more powerful and available on different operating systems.

To learn more about this, check this: https://learn.microsoft.com/en-us/powershell/scripting/install/installing-powershell-on-windows.

Install the App Installer from Microsoft App Store. This will enable the winget tool on the default PowerShell 5.1 and new PowerShell 7.X.Y to be installed.
Open the default Windows PowerShell 5.1 as administrator from the Windows Start menu, then do the following:
```
$ winget search Microsoft.PowerShell
```
This command will return the available PowerShell versions to install. We do not recommend installing the .preview version.
Now install the stable release of PowerShell using the following command:
```
 $ winget install --id Microsoft.Powershell --source winget
```

Windows Terminal

Windows Terminal is a command line tool, available on Microsoft Store (https://apps.microsoft.com/store/apps). Install it from there. You can manage multiple command line environments such as Windows PowerShell 5.1, PowerShell 7.X.Y, CMD, WSL, etc. using a single application.

Visual Studio Code

Visual Studio Code is a cross-platform code editor from Microsoft. You can install different extensions within VS Code to enable features for code development such as remote SSH, debugging, compiling, etc.

Download VS Code from here: https://code.visualstudio.com/download for your operating system. Follow graphical instructions for installation.
If you want to open an empty file in your current working directory using VS Code, then type:
```
$ code .
```
To open a file using VS Code from the terminal, go to the directory from terminal and type:
```
$ code filename.ext
```
Once installed, add the extension packs for Python, Remote Development, and Jupyter, from Microsoft. These packages will be necessary for smooth operation.

Windows Subsystem for Linux (WSL)

The current stable version for Windows Subsystem for Linux is WSL2 and this is the default installation. Open PowerShell 7.X.Y (your current installation version) as administrator using the Terminal app from the Windows Start menu and then type the following command:
```
$ wsl --list --online
```
This command will show you currently available Linux distributions on Windows.
Install the latest LTS version of Ubuntu which is Ubuntu 22.04.02 LTS:
```
$ wsl --install -d Ubuntu
```
It will ask you to create an user account and set a password. The installation process is fast and straightforward.
Once Ubuntu in WSL is installed, you can use it similar to a regular Ubuntu distribution. To run Ubuntu, open it from the Terminal application option. If this is your first time using Linux, you can familiarize yourself with some commands and operations from here https://ubuntu.com/tutorials/command-line-for-beginners.
Now update the Ubuntu distribution and install two packages for WSL virtual display settings.
```
$ sudo apt update && upgrade
$ sudo apt install xvfb libgl1-mesa-glx
```
The first command will ask your password. Proceed as needed.
To open Windows like file explorer from Ubuntu, type:
```
$ explorer.exe .
```
You can open the WSL home directory and browse, copy, and move files like Windows.
Once you have installed Ubuntu in WSL and VS Code, you can follow these tutorials to get yourself more familiarized with the VS Code environments and capabilities in WSL https://learn.microsoft.com/en-us/windows/wsl/tutorials/wsl-vscode and https://code.visualstudio.com/docs/remote/wsl-tutorial.
To use packages and libraries install in WSL, start VS Code from Ubuntu terminal.

Anaconda on Linux (WSL) and macOS

If this is the first time you are using Python, then seat back, it is going to get confusing like this xkcd comic. Even if you are experienced in Python, you might find this interesting.

Most of the Python based libraries and packages often depend on other libraries and packages (called dependencies). Installing the right version of those packages and maintaining them is often a complex task even for experienced developers. So, we will use a popular Python distribution, Anaconda, to manage all the Python based libraries and relevant dependencies. Anaconda uses conda package manager and works well with pip (Python’s default package manager). Installation of Anaconda comes with popular Python packages such as NumPy, SciPy, Matplotlib, and <insert hundred other packages here>. It also come with Jupyter Notebook and Spyder IDE. Anaconda also has a minimalist version, called Miniconda, which is light weight because it only includes the conda manager and a few packages. We strongly recommend installing Anaconda instead of Miniconda

This step is only for macOS. Install xcode command line tools to obtain basic development libraries and features. On macOS terminal, type:
```
(base) $ xcode-select --install
```
Download Anaconda from here based on your operating system and architecture: https://www.anaconda.com/products/distribution.
On macOS, you can download the graphical installer and install it like every other software by following the on-screen instructions. Alternatively, you can download the installation script and using command line to install Anaconda like Linux. Details of the installation procedure is available here: https://docs.anaconda.com/anaconda/install/mac-os/.
For WSL, download the installation script. Open Ubuntu terminal and use the following command to download the script to WSL home directory:
```
$ wget https://repo.anaconda.com/archive/Anaconda3-2023.03-Linux-x86_64.sh
```
Anaconda3-2023.03-Linux-x86_64 is the latest version of Anaconda for Linux available at the time this is being written. Check for the versions here: https://repo.anaconda.com/archive/. Replace it with the current stable version for download and installation.
Once it is copied in the home directory, you can run the following command on Ubuntu terminal for installation:
```
$ bash Anaconda3-2023.03-Linux-x86_64
```
It will ask you to read the license agreement and your permission for installation. Proceed as needed.
Close the Ubuntu terminal and open it back, you will see the base environment for Anaconda is now available. This is how your terminal is going to look like:
```
(base) $ 
```
Check out these operations and commands for using Conda: https://docs.conda.io/projects/conda/en/4.6.0/_downloads/52a95608c49671267e40c689e0bc00ca/conda-cheatsheet.pdf

`FEniCSx` on Linux and macOS

Once Anaconda is properly installed, create an environment for FEniCSx. In addition to the dolfinx library, we will install mpich, pyvista, cycler, and matplotlib. mpich allows parallel processing of different operations withinFEniCSx and the other three packages are used for quick visualization. Standard installation of Anaconda already comes with these three packages but we will still need to install them inside the FEniCSx environment.
```
(base)    $ conda create -n fenicsx
(base)    $ conda activate fenicsx
(fenicsx) $ conda install -c conda-forge fenics-dolfinx mpich pyvista matplotlib cycler
```
pyvista supports plotting higher order unstructured mesh in Jupyter notebook environment. matplotlib lacks support for higher order unstructured mesh. So, it is recommended to use pyvista for quick visualization. But you can still use matplotlib for regular plotting.
To uninstall FEniCSx packages from Anaconda, you will have to uninstall everything within the environment. Before you proceed to uninstall check if FEniCSx environment is active in the terminal. If it is active, then deactivate it first and proceed to uninstall the packages.
```
(fenicsx) $ conda deactivate
(base)    $ conda remove -n fenicsx --all
(base)    $ conda clean --all
```
It will ask your permission; proceed as needed. FEniCSx should be completely uninstalled now.

Legacy `FEniCS` on Linux and macOS (optional)

A lots of the tutorials, examples, and published codes are still written in legacy FEniCS. So, you may want to install the legacy version in case you want to run codes written in legacy FEniCS.

Installation process is similar to FEniCSx. Since higher order mesh wasn’t a feature for legacy FEniCS, we are skipping the installation of pyvista here. Necessary visualization can be done using matplotlib.
```
(base)   $ conda create -n fenics
(base)   $ conda activate fenics
(fenics) $ conda install -c conda-forge fenics matplotlib cycler
```

Uninstallation procedure for legacy FEniCS is also similar to the FEniCSx package.

(fenics) $ conda deactivate
(base)   $ conda remove -n fenics --all
(base)   $ conda clean --all

An alternative way to install on Ubuntu (not recommended)

On Ubuntu, we can also install FEniCSx using apt package manager. Albeit the installation process being simple and lightweight, FEniCSx version available via apt is often not the latest version. So, we do not recommend installing this way.
```
$ sudo add-apt-repository ppa:fenics-packages/fenics
$ sudo apt update
$ sudo apt install fenicsx
```

To uninstall FEniCSx using apt on Ubuntu, follow the procedures below:

$ sudo apt remove fenicsx
$ sudo apt remove --auto-remove fenicsx
$ sudo apt purge fenicsx
$ sudo apt purge --auto-remove fenicsx

Legacy FEniCS can be installed using this approach as well. Please make sure to use fenics instead of fenicsx in the command line for installing and uninstalling legacy FEniCS.

Test your `FEniCSx` installation

Now we will run a simple FEniCSx example code to test the installation. If you open Ubuntu or macOS terminal now, you will see the (base) environment is active. So, you have to activate the (fenicsx) environment before running the code.
```
(base) $ conda activate fenicsx
```
Now we should see:
```
(fenicsx) $ 
```
In case you close your terminal and reopen it, you will see the (base) environment is active by default. You will have to activate (fenicsx) environment using the above command.
Create a directory called fenicsx-code in our WSL home directory and navigate to it:
```
(fenicsx) $ mkdir fenicsx-code
(fenicsx) $ cd fenicsx-code
```

Copy the following python code and save it poisson.py using VS Code in the above directory. This code solves a simple 2D Poisson problem. Technical details of this code is described here: https://jsdokken.com/dolfinx-tutorial/chapter1/fundamentals.

 import os
 import numpy
 import ufl
 import dolfinx
 from dolfinx import mesh, fem, io, plot 
 from mpi4py import MPI
 from petsc4py import PETSc
 import pyvista as pv

 # clears the terminal and prints dolfinx version
 os.system('clear')
 # prints dolfinx version
 print(f"DOLFINx version: {dolfinx.__version__}")

 # no of elements in each direction
 NElem   = 8

 # create a unit square with 8x8 elements with quad elements and use first order shape function
 domain  = mesh.create_unit_square(MPI.COMM_WORLD,NElem,NElem,mesh.CellType.quadrilateral)
 V       = fem.FunctionSpace(domain,("CG",1))

 ## define trial and test functions
 u       = ufl.TrialFunction(V)
 v       = ufl.TestFunction(V)

 # source term of the poisson equation
 f       = fem.Constant(domain, PETSc.ScalarType(-6))

 ## applying boundary conditions
 uD      = fem.Function(V)
 uD.interpolate(lambda x: 1 + x[0]**2 + 2 * x[1]**2)
 tdim    = domain.topology.dim
 fdim    = tdim - 1
 domain.topology.create_connectivity(fdim, tdim)
 boundary_facets = mesh.exterior_facet_indices(domain.topology)
 boundary_dofs   = fem.locate_dofs_topological(V, fdim, boundary_facets)
 bc      = fem.dirichletbc(uD, boundary_dofs)

 # bilinear form
 a       = ufl.dot(ufl.grad(u), ufl.grad(v)) * ufl.dx
 L       = f * v * ufl.dx

 # set PETSc solver options
 sol_opts = {"ksp_type": "preonly", "pc_type": "lu"}
 # formulate the problem
 problem = fem.petsc.LinearProblem(a, L, bcs=[bc], petsc_options=sol_opts)
 # solve the problem
 uh = problem.solve()

 ## error calculation
 V2          = fem.FunctionSpace(domain, ("CG", 2))
 uex         = fem.Function(V2)
 uex.interpolate(lambda x: 1 + x[0]**2 + 2 * x[1]**2)

 L2_error    = fem.form(ufl.inner(uh - uex, uh - uex) * ufl.dx)
 error_local = fem.assemble_scalar(L2_error)
 error_L2    = numpy.sqrt(domain.comm.allreduce(error_local, op=MPI.SUM))

 error_max   = numpy.max(numpy.abs(uD.x.array-uh.x.array))

 # print the error
 if domain.comm.rank == 0:
     print(f"Error_L2 : {error_L2:.2e}")
     print(f"Error_max : {error_max:.2e}")

 # writing output files in xdmf format
 with io.XDMFFile(domain.comm, "output.xdmf", "w") as xdmf:
     xdmf.write_mesh(domain)
     xdmf.write_function(uh)

 # 2D contour plots of the mesh and result using pyvista
 #pv.start_xvfb()    # Uncomment the line on WSL
 pv.off_screen = True
 topology, cell_types, geometry = plot.create_vtk_mesh(domain, tdim)
 grid = pv.UnstructuredGrid(topology, cell_types, geometry)

 plotter = pv.Plotter()
 plotter.add_mesh(grid,show_edges=True)
 plotter.view_xy()
 plotter.save_graphic('mesh.pdf')

 u_topology, u_cell_types, u_geometry = plot.create_vtk_mesh(V)
 u_grid = pv.UnstructuredGrid(u_topology, u_cell_types, u_geometry)
 u_grid.point_data["u"] = uh.x.array.real
 u_grid.set_active_scalars("u")
 u_plotter = pv.Plotter()
 u_plotter.add_mesh(u_grid,show_edges=True)
 u_plotter.view_xy()
 u_plotter.save_graphic('contour.pdf')

Now run the python code from the Ubuntu terminal:
```
(fenicsx) $ python3 poisson.py
```
This should save .h5 and .xdmf files with the results and save the mesh and contour plot of the primary variable .pdf files in the working directory.

What is FEniCSx